Four states — Georgia, Louisiana, Mississippi and Texas — would again have to get approval from the Justice Department before making any changes in the way they hold elections under a bipartisan bill introduced Thursday to restore parts of the Voting Rights Act that the Supreme Court struck down as unconstitutional.

Supporters said the bill would modernize and improve the 1965 civil rights legislation by updating a formula used to require certain states with a history of discrimination to get federal approval before changing election laws and practices.

The Supreme Court ruled last June that the existing formula that had become the government’s primary tool in enforcing the law relied on four-decade-old data that didn’t reflect racial progress and other changes in society.

“What we were facing was both a constitutional as well as a political challenge,” said Rep. James Sensenbrenner (R-Wis.), who helped write the bill along with Rep. John Conyers (D-Mich.) and Senate Judiciary Committee Chairman Patrick Leahy (D-Vt.) “I think we have threaded that needle.”

The new bill redraws from scratch the formula used to determine which states are required to seek federal approval before changing their voting practices. It requires clearance only from states where there have been at least five Voting Rights Acts violations in the most recent 15 years — with at least one committed by the state itself.

Supporters said only Georgia, Louisiana, Mississippi and Texas fall into that category. After 10 years, states could seek a “bailout” from the clearance requirement.

Counties and municipalities would be covered in the new formula if found to have committed three Voting Rights Act violations in the most recent 15 years. One violation would suffice if the violation occurred in an area with a “persistent and extremely low minority voter turnout.”

The provision knocked down by the Supreme Court required federal clearance by the states of Alabama, Alaska, Arizona, Georgia, Louisiana, Mississippi, South Carolina, Texas and Virginia as well as certain counties in California, Florida, New York, North Carolina and South Dakota, and some local jurisdictions in Michigan.

Lawmakers said they introduced the bill to coincide with Monday’s holiday commemorating Martin Luther King Jr.’s birth. They were joined by Rep. John Lewis (D-Ga.), who had been a leader in the civil rights movement.

“It is amazing to me, almost unreal, that we were able to come together so quickly,” Lewis said.

Leahy will take the lead on the bill in the Senate. The legislation, he said, would ensure that any state that committed continued violations in the future could face clearance requirements and “protect against discrimination in every state, all 50.”

Leahy said he was optimistic about the bill’s path in the Democratic-controlled Senate but acknowledged he hasn’t secured a Republican co-sponsor. He said he’d spoken to several Republicans who support the measure and would vote for it on the Senate floor.

The path for the bill in the GOP-led House is less certain. Sensenbrenner said he had spoken with some Southern members of the House Republican caucus who expressed support and may sign on as co-sponsors.

When asked if House GOP leaders support the bill, Sensenbrenner replied, “They cogitate and think.” He added: “I’m here to say this is the right thing to do.”

Voting rights groups generally praised the attempt to forge a compromise. But some said the law should be made even stronger.

“While the start of a critical debate on voting, the bill represents a floor, and not a ceiling, for ensuring that elections are free, fair and accessible to all Americans,” said Judith Browne Dianis, co-director of the Advancement Project.

The bill also would set new standards for states to meet in publishing changes to election laws and procedures. It would give federal courts more leeway to determine violations, allowing judges to cite not just intentional violations but also those that effectively result in discrimination even if that was not the intent.

The bill also would make it easier to obtain injunctions to stop changes in voting laws.

In a bid to secure GOP support, the bill includes an exemption for voter identification laws. Under the bill, states would be allowed to pursue laws requiring voters to show identification. If such a law were struck down, it would not count against states’ tally of voting rights violations.

Sensenbrenner said the result was a package designed to win passage in both houses.

“This is a good compromise,” he said. “Patrick Leahy is about as liberal as I am conservative.”

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